Linear Operators: General theory |
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Page 2
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B but not in A , i.e. , the set { x | x e B , x ¢ A } . This set is sometimes denoted by B - A . In a discussion where ...
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B but not in A , i.e. , the set { x | x e B , x ¢ A } . This set is sometimes denoted by B - A . In a discussion where ...
Page 261
... mean that f ( s ) ≥ g ( s ) for all s in S. Finally , C * ( S ) is partially ordered by defining * y * to mean that a * fy * f for every ƒ e C ( S ) with f≥ 0 . Before representing the conjugate space C * ( S ) we first observe that ...
... mean that f ( s ) ≥ g ( s ) for all s in S. Finally , C * ( S ) is partially ordered by defining * y * to mean that a * fy * f for every ƒ e C ( S ) with f≥ 0 . Before representing the conjugate space C * ( S ) we first observe that ...
Page 660
... mean and pointwise convergence theorems for the contin- uous case . Section 8 is concerned with a certain class of operators T for which the sequence of averages ( N - 1 NT " } converges in the uniform topology of operators . Finally ...
... mean and pointwise convergence theorems for the contin- uous case . Section 8 is concerned with a certain class of operators T for which the sequence of averages ( N - 1 NT " } converges in the uniform topology of operators . Finally ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ